Question

The area of a rectangle knitted blanket is 9x^2-6x-8. What are the possible dimensions of the blanket? Use factoring ​

Answer 1

Answer:

(3x-4) by (3x+2) or (-3x+4) by (-3x-2)

Step-by-step explanation:

To factor 9x^2-6x-8 we want to find the factors of 9 and the factors of -8 that when multiplied in sequence and then added give us -6.

factors of -8:

-8 & 1

8  & -1

-4  & 2

4  & -2

you might also want to remember that these can be flipped, so if you have -8 & 1 you can also have 1 &-8.

factors of 9:

9  &  1

-9  & -1

3  &  3

-3  &  -3

So now we just need to find numbers where

a & b are factors of 9 and c & d are factors of -8 and a*c+b*d=-6,

if that is the case then (ax+c)*(bx+d)=9x^2-6x-8

guess: 3 & 3 and -4 & 2

3*(-4) + 3*2=-12 +6 = -6

so one factoring is (3x-4)*(3x+2)

This means that one of the possible dimensions of the blanket is (3x-4) by (3x+2)

guess: -3 & -3 and 4 & -2

(-3)*4+(-3)*(-2)= -12+6 = -6

so another factoring is (-3x+4)*(-3x-2)

So you could also have a blanket with dimensions (-3x+4) by (-3x-2) but this might not make sense to do because, if you input positive numbers for x you will get negative dimensions which in the real world don't exist for a knitted blanket.

p.s sorry for the late response.